학술논문
Fundamental solution and Fourier series in eigenfunctions of degenerate elliptic operator
Document Type
Author abstract
Author
Source
Journal of Mathematical Analysis and Applications. May 1, 2007, Vol. 329 Issue 1, p132, 13 p.
Subject
Language
English
ISSN
0022-247X
Abstract
To link to full-text access for this article, visit this link: http://dx.doi.org/10.1016/j.jmaa.2006.06.014 Byline: V.S. Serov Keywords: Fundamental solution; Spectral theorem; Fourier series Abstract: We study the degenerate elliptic differential operator of the second order in the divergence form. The operator is assumed to be symmetric. The weight function which is describing the degeneration of the coefficients (or singularity) assumed to be in the Muckenhoupt class. We prove the uniform estimates for the fundamental solution of this operator and obtain the conditions which guarantee the absolute and uniform convergence of Fourier series in eigenfunctions. These results might be applied to the ground of Fourier method. Author Affiliation: Department of Mathematical Sciences, University of Oulu, PO Box 3000, FIN-90014 Oulu, Finland Article History: Received 6 December 2005 Article Note: (miscellaneous) Submitted by R.H. Torres